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// Copyright (c) The cargo-guppy Contributors
// SPDX-License-Identifier: MIT OR Apache-2.0
use petgraph::{
graph::IndexType,
prelude::*,
visit::{
GraphRef, IntoNeighborsDirected, IntoNodeIdentifiers, NodeCompactIndexable, VisitMap,
Visitable, Walker,
},
};
use std::marker::PhantomData;
/// A cycle-aware topological sort of a graph.
#[derive(Clone, Debug)]
pub struct TopoWithCycles<Ix> {
// This is a map of each node index to its corresponding topo index.
reverse_index: Box<[usize]>,
// Prevent mixing up index types.
_phantom: PhantomData<Ix>,
}
impl<Ix: IndexType> TopoWithCycles<Ix> {
pub fn new<G>(graph: G) -> Self
where
G: GraphRef
+ Visitable<NodeId = NodeIndex<Ix>>
+ IntoNodeIdentifiers
+ IntoNeighborsDirected<NodeId = NodeIndex<Ix>>
+ NodeCompactIndexable,
G::Map: VisitMap<NodeIndex<Ix>>,
{
// petgraph's default topo algorithms don't handle cycles. Use DfsPostOrder which does.
let mut dfs = DfsPostOrder::empty(graph);
// A node is a root iff it has no incoming neighbors *other than
// itself* -- a self-loop is internal to the node's own (single-
// element) SCC and must not disqualify it from being a root. This
// matches `Sccs::externals`'s single-node SCC branch in
// `petgraph_support::scc`.
let roots = graph
.node_identifiers()
.filter(move |&a| !graph.neighbors_directed(a, Incoming).any(|n| n != a));
dfs.stack.extend(roots);
let mut topo: Vec<NodeIndex<Ix>> = (&mut dfs).iter(graph).collect();
// dfs returns its data in postorder (reverse topo order), so reverse that for forward topo
// order.
topo.reverse();
// Because the graph is NodeCompactIndexable, the indexes are in the range
// (0..graph.node_count()).
// Use this property to build a reverse map.
let mut reverse_index = vec![0; graph.node_count()];
topo.iter().enumerate().for_each(|(topo_ix, node_ix)| {
reverse_index[node_ix.index()] = topo_ix;
});
// topo.len cannot possibly exceed graph.node_count().
assert!(
topo.len() <= graph.node_count(),
"topo.len() <= graph.node_count() ({} is actually > {})",
topo.len(),
graph.node_count(),
);
if topo.len() < graph.node_count() {
// This means there was a multi-node cycle in the graph which caused some nodes to be
// skipped: none of its members appears as a root (each has a non-self incoming edge),
// so the DFS never starts inside it. (Self-loops on otherwise-root nodes are handled
// by the root predicate above, matching `Sccs::externals`.)
//
// In this case, do a best-effort job: fill in the missing nodes with their reverse
// index set to the end of the topo order. We could do something fancier here with sccs,
// but for guppy this should never happen in practice. (In fact, the one time this code
// was hit there was actually an underlying bug.)
//
// Cross-check the claim above: every missing node must have at least one non-self
// incoming neighbor. If that's not true, the root predicate dropped a node that
// should have been a root, and the descendants of that dropped root are now being
// mis-placed at the end of the topo order. The proptest above only checks index
// uniqueness, not topological correctness, so without this assertion such a
// regression would pass tests silently.
debug_assert!(
graph.node_identifiers().all(|m| {
dfs.finished.is_visited(&m)
|| graph.neighbors_directed(m, Incoming).any(|p| p != m)
}),
"topo fallback: a node was missed by the DFS but has no non-self incoming \
neighbor, which means the root-set predicate dropped a legitimate root",
);
let mut next = topo.len();
for n in 0..graph.node_count() {
let a = NodeIndex::new(n);
if !dfs.finished.is_visited(&a) {
// a is a missing index.
reverse_index[a.index()] = next;
next += 1;
}
}
}
Self {
reverse_index: reverse_index.into_boxed_slice(),
_phantom: PhantomData,
}
}
/// Sort nodes based on the topo order in self.
#[inline]
pub fn sort_nodes(&self, nodes: &mut [NodeIndex<Ix>]) {
nodes.sort_unstable_by_key(|node_ix| self.topo_ix(*node_ix))
}
#[inline]
pub fn topo_ix(&self, node_ix: NodeIndex<Ix>) -> usize {
self.reverse_index[node_ix.index()]
}
}
#[cfg(test)]
mod tests {
use super::*;
use petgraph::Graph;
/// A self-loop on a node with no other incoming edges must not
/// disqualify it from being a root. Without the fix, the node was
/// filtered out of the root set, its descendants were never visited
/// by the DFS, and the best-effort fallback placed them in node-
/// insertion order -- which can disagree with topological order.
#[test]
fn topo_self_loop_root_orders_descendants_correctly() {
// Insert `b` (index 0) before `a` (index 1) so that node-index
// order *disagrees* with topological order: the edge `a -> b`
// means `a` should precede `b`.
let mut graph = Graph::<(), (), Directed, u32>::new();
let b = graph.add_node(());
let a = graph.add_node(());
graph.add_edge(a, b, ());
graph.add_edge(a, a, ());
let topo = TopoWithCycles::<u32>::new(&graph);
assert!(
topo.topo_ix(a) < topo.topo_ix(b),
"a should precede b in topo order despite the self-loop on a \
(got topo_ix(a)={}, topo_ix(b)={})",
topo.topo_ix(a),
topo.topo_ix(b),
);
}
/// The fallback path (`topo.len() < graph.node_count()`) fires for
/// multi-node cycles with no external entry. Verifies that the
/// debug-only invariant assertion does not false-positive on this
/// legitimate case, and that every node still gets a unique topo
/// index.
#[test]
fn topo_multi_node_cycle_no_external_entry_fallback() {
// a <-> b, plus an unrelated root c. The cycle {a, b} is
// unreachable from c, so neither member is a root and the DFS
// never enters the cycle. The fallback places a and b at the
// end of the topo order.
let mut graph = Graph::<(), (), Directed, u32>::new();
let a = graph.add_node(());
let b = graph.add_node(());
let c = graph.add_node(());
graph.add_edge(a, b, ());
graph.add_edge(b, a, ());
let topo = TopoWithCycles::<u32>::new(&graph);
// All three nodes get unique topo indexes in 0..3.
let mut seen = [false; 3];
for node in [a, b, c] {
let ix = topo.topo_ix(node);
assert!(ix < 3, "topo_ix out of range: {ix}");
assert!(!seen[ix], "topo_ix {ix} seen twice");
seen[ix] = true;
}
// `c` is the only real root, so it must come first.
assert_eq!(
topo.topo_ix(c),
0,
"c should be at the start of the topo order (got {})",
topo.topo_ix(c),
);
}
/// A self-loop on a node that is *also* reachable from a real root
/// must not change anything: the existing root drives the DFS and
/// the self-loop is ignored.
#[test]
fn topo_self_loop_on_non_root_is_harmless() {
// b -> a, plus a self-loop on a. `b` is the only root; `a` is
// visited via b's outgoing edge.
let mut graph = Graph::<(), (), Directed, u32>::new();
let a = graph.add_node(());
let b = graph.add_node(());
graph.add_edge(b, a, ());
graph.add_edge(a, a, ());
let topo = TopoWithCycles::<u32>::new(&graph);
assert!(
topo.topo_ix(b) < topo.topo_ix(a),
"b should precede a in topo order (got topo_ix(b)={}, topo_ix(a)={})",
topo.topo_ix(b),
topo.topo_ix(a),
);
}
}
#[cfg(all(test, feature = "proptest1"))]
mod proptests {
use super::*;
use proptest::prelude::*;
proptest! {
#[test]
fn graph_topo_sort(graph in possibly_cyclic_graph()) {
let topo = TopoWithCycles::new(&graph);
let mut nodes: Vec<_> = graph.node_indices().collect();
check_consistency(&topo, graph.node_count());
topo.sort_nodes(&mut nodes);
for (topo_ix, node_ix) in nodes.iter().enumerate() {
assert_eq!(topo.topo_ix(*node_ix), topo_ix);
}
}
}
fn possibly_cyclic_graph() -> impl Strategy<Value = Graph<(), ()>> {
// Generate a graph in adjacency list form. N nodes, up to N**2 edges.
(1..=100usize)
.prop_flat_map(|n| {
(
Just(n),
prop::collection::vec(prop::collection::vec(0..n, 0..n), n),
)
})
.prop_map(|(n, adj)| {
let mut graph =
Graph::<(), ()>::with_capacity(n, adj.iter().map(|x| x.len()).sum());
for _ in 0..n {
// Add all the nodes under consideration.
graph.add_node(());
}
for (src, dsts) in adj.into_iter().enumerate() {
let src = NodeIndex::new(src);
for dst in dsts {
let dst = NodeIndex::new(dst);
graph.update_edge(src, dst, ());
}
}
graph
})
}
fn check_consistency(topo: &TopoWithCycles<u32>, n: usize) {
// Ensure that all indexes are covered and unique.
let mut seen = vec![false; n];
for i in 0..n {
let topo_ix = topo.topo_ix(NodeIndex::new(i));
assert!(
!seen[topo_ix],
"topo_ix {topo_ix} should be seen exactly once, but seen twice"
);
seen[topo_ix] = true;
}
for (i, &this_seen) in seen.iter().enumerate() {
assert!(this_seen, "topo_ix {i} should be seen, but wasn't");
}
}
}